Difference between solutions of linear equations and solutions of linear in equalities

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Natalie Stanley

Mathematics

7 June, 20:52

Difference between solutions of linear equations and solutions of linear in equalities

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Paulina Sharp · Answer 1

A linear equation is any equation involving one or two variables whose exponents are one. In the case of one variable, one solution exists for the equation. For example, with 2_x_ = 6, x can only be 3.

One obvious difference between linear equations and inequalities is the solution set. A linear equation of two variables can have more than one solution.

For instance, with x = 2_y_ + 3, (5, 1), then (3, 0) and (1, - 1) are all solutions to the equation.

In each pair, x is the first value and y is the second value. However, these solutions fall on the exact line described by y = ½ x - 3/2.

If the inequality were x? 2_y_ + 3, the same linear solutions just given would exist in addition to (3, - 1), (3, - 2) and (3, - 3), where multiple solutions can exist for the same value of x or the same value of y only for inequalities. The "?" means that it is unknown whether x is greater than or less than 2_y_ + 3. The first number in each pair is the x value and the second is the y value.